Entropy generation isolated system

The objective function (13) representing the total dissipation of kinetic energy of the flows at isothermal motion of fluid is proportional to the entropy production in the circuit and its transfer to the environment, i.e., proportional to the entropy accumulated by the isolated system (interconnection of the circuit and environment). The matrix equation (14) describes the first Kirchhoff law, which, as applied to hydraulic circuits, expresses the requirement for mass conservation. Equality (15) represents a balance between the energy generated and consumed in the circuit. 

These equations indicate that a maximum of entropy is achieved at equilibrium. On the other hand, if we demand an isolated system that is even not transparent for entropy, then we must conclude that under such circumstances entropy will be generated, if such as system is moving toward equilibrium. We have used here the principle of maximum entropy under the constraints of constant energy and constant volume. 

Entropy generation is considered a key concept of nonequiHbrium thermodynamics. Let us view entropy generation for the following cases isolated systems, systems in a homogeneous thermostat, and systems in a nonhomogeneous environment (in the temperature gradient field, in chemical potential field, etc.). At that, let us divide systems into two types weakly nonequilibrium (linear) and far from equilibrium (nonlinear). 

Our thermodynamic-information derivation based on a heat cycle demonstrates the fact that it is impossible, in the type of channel considered, for the bound (2 15) information contained in an input message to be transferred without its (average) loss. Such information transfer can be worsened only by heat dissipation of energy, which means by noise heat (AQo > 0) generated by the irreversible processes in the channel [described by a transformer C of input heat, which has non-ideal properties (inner friction)]. Simultaneously the whole thermodynamic entropy of the extended isolated system in which this process is running increases, and maximum average value of the output transferred information diminishes (7). 

If this result information is used again the less information is generated etc. But, contemporarily, any run of the cycle generates the positive addition of entropy (thermodynamic) of a wider isolated system in which this transformation (transfer) runs (44),... 

Self-organization seems to be counterintuitive, since the order that is generated challenges the paradigm of increasing disorder based on the second law of thermodynamics. In statistical thermodynamics, entropy is the number of possible microstates for a macroscopic state. Since, in an ordered state, the number of possible microstates is smaller than for a more disordered state, it follows that a self-organized system has a lower entropy. However, the two need not contradict each other it is possible to reduce the entropy in a part of a system while it increases in another. A few of the system s macroscopic degrees of freedom can become more ordered at the expense of microscopic disorder. This is valid even for isolated, closed systems. Eurthermore, in an open system, the entropy production can be transferred to the environment, so that here even the overall entropy in the entire system can be reduced. 

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